QJEEM25Mab690: JEE Main 2025 Mathematics - Class 11 JEEM25Mab690 Solution: Let and . Then the domain of is

Question

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Let $f(x)=\log _{\mathrm{e}} x$ and $g(x)=\frac{x^4-2 x^3+3 x^2-2 x+2}{2 x^2-2 x+1}$ . Then the domain of $f \circ g$ is

Accepted Answer

$\begin{aligned}& f(x)=\ln x \\& g(x)=\frac{x^4-2 x^3+3 x^2-2 x+2}{2 x^2-2 x+1} \\& D_g \in R \\& D_f \in(0, \infty)\end{aligned}$

For $D_{f o g} \Rightarrow g(x)>0$

$\begin{aligned}& \frac{x^4-2 x^3+3 x^2-2 x+2}{2 x^2-2 x+1}>0 \\& \Rightarrow x^4-2 x^3+3 x^2-2 x+2>0\end{aligned}$

Clearly $\mathrm{x}<0$ satisfies which are included in option (1) only.

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